AsCl₃ is a molecular compound. Hence, it is written in molecular form.
H₂O is a molecular compound. Hence, it is written in molecular form.
HCl is a strong acid which completely dissociates in water. Hence, it is written in ionic form, i.e. H⁺ and Cl⁻
As(OH)₃ in a weak acid with pKₐ = 9.2, and most of As(OH)₃ in aqueous solution exists as molecules. Hence, it is written in molecular form.